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Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights

  • Book
  • © 2018

Overview

Authors:
  1. Eli Levin

    1. Department of Mathematics, Open University of Israel, Tel-Aviv, Israel

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    You can also search for this author in PubMed   Google Scholar

  2. Doron S. Lubinsky

    1. Mathematics, Georgia Institution of Technology, Atlanta, USA

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    You can also search for this author in PubMed   Google Scholar

  • One of the first books of its kind published on the topic
  • Provides a general treatment of varying exponential weights
  • Appeals to a wide range of researchers as well as young mathematicians

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. Introduction

    • Eli Levin, Doron S. Lubinsky
    Pages 1-8

  3. Statement of Main Results

    • Eli Levin, Doron S. Lubinsky
    Pages 9-12

  4. Potential Theoretic Estimates

    • Eli Levin, Doron S. Lubinsky
    Pages 13-27

  5. Restricted Range Inequalities

    • Eli Levin, Doron S. Lubinsky
    Pages 29-35

  6. Bounds for Christoffel Functions

    • Eli Levin, Doron S. Lubinsky
    Pages 37-45

  7. Spacing of Zeros

    • Eli Levin, Doron S. Lubinsky
    Pages 47-51

  8. Bounds on Orthogonal Polynomials

    • Eli Levin, Doron S. Lubinsky
    Pages 53-62

  9. Markov-Bernstein Inequalities in L ∞

    • Eli Levin, Doron S. Lubinsky
    Pages 63-65

  10. Discretization of Potentials

    • Eli Levin, Doron S. Lubinsky
    Pages 67-82

  11. Derivatives of Discretized Polynomials

    • Eli Levin, Doron S. Lubinsky
    Pages 83-92

  12. Weighted Polynomial Approximations

    • Eli Levin, Doron S. Lubinsky
    Pages 93-115

  13. Formulae Involving Bernstein-Szegő Polynomials

    • Eli Levin, Doron S. Lubinsky
    Pages 117-122

  14. Asymptotics of Orthonormal Polynomials

    • Eli Levin, Doron S. Lubinsky
    Pages 123-142

  15. Further Bounds

    • Eli Levin, Doron S. Lubinsky
    Pages 143-151

  16. Universality Limits and Entropy Integrals

    • Eli Levin, Doron S. Lubinsky
    Pages 153-164

  17. Back Matter

    Pages 165-170
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Keywords

About this book

This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals.  Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics. 

This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices. 

Reviews

“This book is written by two well-reputed specialists on orthogonal polynomials. Thus, It will be of great interest to those studying orthogonal polynomials, as well as Ph.D. students specializing in this or related areas. The structure of the text is nice. In fifteen short chapters the authors provide us with the statement of the results and their corresponding proofs in a rigorous and precise way.” (Juan José Monero-Balcázar, Mathematical Reviews, October, 2018)​

Authors and Affiliations

  • Department of Mathematics, Open University of Israel, Tel-Aviv, Israel

    Eli Levin

  • Mathematics, Georgia Institution of Technology, Atlanta, USA

    Doron S. Lubinsky

About the authors

Eli Levin is an emeritus professor at the Open University of Israel in Ramat Aviv. 

Doron Lubinsky is a professor at Georgia Institute of Technology. Both are authors of papers on approximation theory, and a joint monograph on orthogonal polynomials.

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